After installing Service Pack 2 for ArcGIS Desktop 9.3.1, opening a map document from Windows Explorer, ArcCatalog, Windows Desktop, Windows Recent Documents, or the Web does not open it in a new ArcMap session. So, if an existing map document is opened, ArcMap opens as expected; however, if another map document is now opened, a new instance of ArcMap is not started. Instead, the map document is sent to the existing instance.
This is a known issue. For updates on the status, use bug number NIM059009. To work around this issue, follow the instructions below.